Q. 74.5( 4 Votes )

# <span lang="EN-US

Answer :

Formula used

Isosceles triangle property

If 2 angles of triangle are equal then their corresponding sides are also equal

Perpendicular drawn through tangent pass through centre

Solution

In Δ QPO

QOP = 90°

By angle sum property

QOP + QPO + OQP = 180°

QPO = 90° - OQP

In Δ QOR

As OQ = OR radius of same circle

OQP = ORP

As RS is tangent

ORS = 90°

In Δ SPR

SPR = OPQ (Vertically opposite angles)

SPR = 90° - OQP

SRP = ORS - ORP

= 90° - OQP

Hence;

SPR = SRP

By isosceles triangle property

SR = SP

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